{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Interpolation\n",
      "======================================================================\n",
      "\n",
      "Using B-splines in scipy.signal\n",
      "-------------------------------\n",
      "\n",
      "Example showing how to use B-splines in scipy.signal to do\n",
      "interpolation. The input points must be equally spaced to use these\n",
      "routine."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import r_, sin\n",
      "from scipy.signal import cspline1d, cspline1d_eval\n",
      "%pylab inline\n",
      "\n",
      "x = r_[0:10]\n",
      "dx = x[1]-x[0]\n",
      "newx = r_[-3:13:0.1]  # notice outside the original domain \n",
      "y = sin(x) \n",
      "cj = cspline1d(y)\n",
      "newy = cspline1d_eval(cj, newx, dx=dx,x0=x[0]) \n",
      "from pylab import plot, show\n",
      "plot(newx, newy, x, y, 'o') \n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7dBEdlTzuuw/o2hUoKBAdiXKonq8elPTvoby8HLNmzUJmZiYOHjyIL774AgV3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\niIFQ0ieEEAOhpE8IIQby/zCdVWT0LzqwAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x295f350>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "N-D interpolation for equally-spaced data\n",
      "-----------------------------------------\n",
      "\n",
      "The scipy.ndimage package also contains spline\\_filter and\n",
      "map\\_coordinates which can be used to perform N-dimensional\n",
      "interpolation for equally-spaced data. A two-dimensional example is\n",
      "given below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import ogrid, sin, mgrid, ndimage, array\n",
      "from matplotlib import pyplot as plt\n",
      "\n",
      "x,y = ogrid[-1:1:5j,-1:1:5j]\n",
      "fvals = sin(x)*sin(y)\n",
      "newx,newy = mgrid[-1:1:100j,-1:1:100j]\n",
      "x0 = x[0,0]\n",
      "y0 = y[0,0]\n",
      "dx = x[1,0] - x0\n",
      "dy = y[0,1] - y0\n",
      "ivals = (newx - x0)/dx\n",
      "jvals = (newy - y0)/dy\n",
      "coords = array([ivals, jvals])\n",
      "newf1 = ndimage.map_coordinates(fvals, coords)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To pre-compute the weights (for multiple interpolation results), you\n",
      "would use"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "coeffs = ndimage.spline_filter(fvals)\n",
      "newf2 = ndimage.map_coordinates(coeffs, coords, prefilter=False)\n",
      "\n",
      "plt.subplot(1,2,1)\n",
      "plt.imshow(newf1)\n",
      "plt.subplot(1,2,2)\n",
      "plt.imshow(newf2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cF66XwfXcO+xxShOBC6gYxWHmACuvocg3vHsinI9rGpin00zkR21mhVoCzCVV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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3b4f410>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Interpolation of an N-D curve\n",
      "-----------------------------\n",
      "\n",
      "The scipy.interpolate packages wraps the netlib FITPACK routines\n",
      "(Dierckx) for calculating smoothing splines for various kinds of data\n",
      "and geometries. Although the data is evenly spaced in this example, it\n",
      "need not be so to use this routine."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import arange, cos, linspace, pi, sin, random\n",
      "from scipy.interpolate import splprep, splev\n",
      "\n",
      "# make ascending spiral in 3-space\n",
      "t=linspace(0,1.75*2*pi,100)\n",
      "\n",
      "x = sin(t)\n",
      "y = cos(t)\n",
      "z = t\n",
      "\n",
      "# add noise\n",
      "x+= random.normal(scale=0.1, size=x.shape)\n",
      "y+= random.normal(scale=0.1, size=y.shape)\n",
      "z+= random.normal(scale=0.1, size=z.shape)\n",
      "\n",
      "# spline parameters\n",
      "s=3.0 # smoothness parameter\n",
      "k=2 # spline order\n",
      "nest=-1 # estimate of number of knots needed (-1 = maximal)\n",
      "\n",
      "# find the knot points\n",
      "tckp,u = splprep([x,y,z],s=s,k=k,nest=-1)\n",
      "\n",
      "# evaluate spline, including interpolated points\n",
      "xnew,ynew,znew = splev(linspace(0,1,400),tckp)\n",
      "\n",
      "import pylab\n",
      "pylab.subplot(2,2,1)\n",
      "data,=pylab.plot(x,y,'bo-',label='data')\n",
      "fit,=pylab.plot(xnew,ynew,'r-',label='fit')\n",
      "pylab.legend()\n",
      "pylab.xlabel('x')\n",
      "pylab.ylabel('y')\n",
      "\n",
      "pylab.subplot(2,2,2)\n",
      "data,=pylab.plot(x,z,'bo-',label='data')\n",
      "fit,=pylab.plot(xnew,znew,'r-',label='fit')\n",
      "pylab.legend()\n",
      "pylab.xlabel('x')\n",
      "pylab.ylabel('z')\n",
      "\n",
      "pylab.subplot(2,2,3)\n",
      "data,=pylab.plot(y,z,'bo-',label='data')\n",
      "fit,=pylab.plot(ynew,znew,'r-',label='fit')\n",
      "pylab.legend()\n",
      "pylab.xlabel('y')\n",
      "pylab.ylabel('z')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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o1bG8/vr/+OefdJ4yTuT7nF0cWPMT/Yf6Qf36kJgIDRroXY5HIfaUv39IkXhq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\nAunpGxrjo1RJzi8hSkjQEBVUd4dT8Wt5OSa0u3acTldu8tD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       "text": [
        "<matplotlib.figure.Figure at 0x3b71e90>"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}